Question

A car is moving with a velocity of 20 ms and
the driver changes gear and increases the
velocity to 30 ms -' in 0.1 s. If the mass of the
car is 1200 kg, then force on the car because of
change of gear is
​

Answer 1

Given :-

• initial velocity of car, u = 20 ms⁻¹
• final velocity of car , v = 30 ms⁻¹
• time taken in velocity change,t = 0.1 s
• mass of Car, m = 1200 kg

To find :-

• force on the car because of gear changing, F = ?

Formula required :-

● First equation of motion

$\boxed{ \orange{ \sf{v = u + at}}}$

(where v is final velocity, u is initial velocity, a is the acceleration and t is the time taken)

● Formula for calculating Force

$\boxed{ \orange{ \sf{F = ma}}}$

(where F is the force, m is the mass and a is the acceleration)

Solution :-

➟ Finding the acceleration of Car

By first equation of motion

$\implies \sf{v = u + at}$

$\implies \sf{30 =20 + a(0.1) }$

$\implies \sf{a = \frac{30 - 20}{0.1} }$

$\implies \red{ \boxed{ \sf{a = 100 \: \: m {s}^{ - 2} }}}$

➟ Calculating the force on the Car due to changing gear

Using formula for calculating force

$\implies \sf{F= ma}$

$\implies \sf{F= 1200 \times 100}$

$\implies \sf{F= 120000 \: N}$

$\implies \red{ \boxed{ \boxed{ \sf{F = 120 \: kN}}}}$

Hence, Car will experience a force of 120 kilo- newton due to the changing of gear.